Displaced people from the minority Yazidi sect, fleeing violence in the Iraqi town of Sinjar, take refuge at Dohuk province. Photograph: Stringer/Iraq/Reuters

US fighter jets and drones struck vehicles and artillery belonging to the Islamic State (Isis) five times on Sunday, bringing the new US air war in Iraq into a fourth day of what President Barack Obama said might be a protracted effort.

As US officials and their allies scrambled to work out a plan to get tens of thousands of Iraqi Yazidis besieged by Isis down from a mountain near the northern town of Sinjar – the UN said on Sunday that 15-20,000 refugees had so far escaped – the latest strikes hit Isis positions in relief of Kurdish fighters aiming to protect the Kurdish regional capital of Irbil.

Later on Sunday the State Department said it had removed some staff from Irbil and Baghdad to Basra, in the south of Iraq, and to the Iraq Support Unit in Amman, Jordan. The US consulate in Irbil and embassy in Baghdad remained open, the department said.

US military officials said the five air strikes took place over approximately five hours early on Sunday. The first, around 2.15am, destroyed an Isis armed truck that had fired on Kurdish peshmerga militia, who have long sought direct US aid. A follow-on strike 30 minutes later hit another armed truck nearby.

Over the next three hours strikes hit mortar positions, destroying one, and several other armed trucks. US Central Command, the regional US military authority conducting the strikes, announced that one armed truck was destroyed and two were damaged by US aircraft. Central Command did not provide locations for those strikes.

On Sunday, a Kurdish official told Reuters that Kurdish forces had taken back two towns in northern Iraq from Isis militants. Hoshiyar Zebari, who claimed the forces had been supported by the US air strikes, said the Kurds had recaptured the towns of Guwair and Makhmur. Asked how long the US would have to continue strikes to help the Kurds defeat Isis, Zebari said: “As President Obama said, there is no time limit.”

Thus far, the vast majority of air strikes have targeted Isis positions threatening Irbil, as several US officials consider the advance of Isis into pro-US Iraqi Kurdistan an unacceptable outcome. Dozens of US special-operations advisers are stationed in Irbil, where the US also has a consulate, and the rationale of protecting that force provides Obama with diplomatic cover for attacks to halt the Isis advance on territory US officials believe must not fall to the Islamic extremists.

Despite Obama’s description of the humanitarian crisis atop Mount Sinjar prompting the newly aggressive US posture, so far only on Saturday have US warplanes hit Isis vehicles harassing Iraqi Yazidis trapped without food or water. Thus far, the US military reports that C-17 and C-130 cargo planes have dropped more than 52,000 meals and 10,600 gallons of fresh water.

The air strikes, described as somewhat less than a concerted campaign, have “at least given pause to Islamic extremists as they advance but much more effort will be required for a positive outcome”, retired US general Carter Ham told ABC News on Sunday.

Isis has made sweeping territorial gains, which have left the Islamist fighters in control of much of central Iraq, reportedly including the massive Mosul dam which could flood the country all the way to Baghdad. Administration officials describe the strikes as short of a broad counterterrorism effort; at least one Pentagon planning effort reported by the Guardian examined striking Isis in Syria as well as Iraq.

Iraq air strikes graphic Photograph: /The Guardian

Isis’s reach into Iraqi Kurdistan “can be stopped by a combination of people on the ground being ready to fight, such as the peshmerga, and American air power”, Ambassador James Jeffrey, a retired Obama-era top diplomat in Baghdad, told CBS News on Sunday.

US officials are liaising with allies to figure out how to break Isis’s siege of tens thousands of Yazidis by establishing a “safe corridor” off the mountain, which Obama has warned will be logistically complex. Obama held phone calls on Saturday to discuss Iraq with the British prime minister, David Cameron, and French president, François Hollande, agreeing “to work together on a longer-term strategy to counter” Isis, the White House said.

The US defence secretary, Chuck Hagel, who is travelling, spoke on Saturday about Iraq with his UK counterpart, Michael Fallon. Rear Admiral John Kirby, the Pentagon press secretary, said the secretaries would “look for additional ways to coordinate military operations”.

The UK government has said it is working on further air drops to those trapped on Mount Sinjar in the coming days after the RAF delivered the first package of British humanitarian aid on Saturday.

Two C-130 Hercules transporters left RAF Brize Norton, in Oxfordshire on Saturday and the same night bundles were delivered, including 1,200 reusable water containers with filtration devices, providing 6,000 litres of clean water in total, and 240 solar lanterns that can also be used to recharge mobile phones.

A Downing Street spokesman said: “We are working to step up these deliveries in the coming days,” he said. “Meanwhile, we continue to engage with the US, Kurds, Turks and other international partners on how to get those trapped on the mountain to safety. And we are planning to increase the number of humanitarian advisers in Irbil to provide better links to the situation on the ground.”

In a handout picture released by the British Ministry of Defence humanitarian aid is loaded ont o a Hercules C-130 transport plane at RAF Brize Norton, north-west of London. Photograph: CPL Neil Bryden/AFP/Getty Images

The spokesman also echoed criticism by the White House of the Iraqi prime minister and former US ally Nouri al-Maliki, urging Iraq “to appoint a prime minister who can lead an inclusive government”.

In an appearance on Iraqi TV on Sunday, Maliki indicated that he would not drop his bid for a third term and accused Iraq’s president, Fuad Masum, of violating the constitution. A US state department official said that it fully supported Masum after Maliki’s comments.

Later, reports were circulating that Maliki had ordered security forces loyal to him to seize important areas around Baghdad, including bridges spanning the Tigris river and installations in the secured Green Zone, further raising concerns that Maliki was determined to retain power.

Brett McGurk, a State Department troubleshooter on Iraq, tweeted: “Fully support president of Iraq Fuad Masum as guarantor of the constitution and a PM nominee who can build a national consensus.” Many observers interpreted McGurk’s comment as a decisive abandonment of the prime minister, whom US officials were instrumental in installing in 2006.

“It’s clear that the United States is breaking from Maliki,” Steven A Cook of the Council on Foreign Relations told CNN.

Vice-president Joseph Biden last spoke with Masum, a Kurd recently installed as president, on Friday. A White House readout said Biden “emphasised the importance of a forming a new government on the constitutional timeline, including a national program that can help consolidate national forces” against Isis.

Barack Obama has long described the formation of a new government as a condition for a deeper US air campaign against Isis, arguing that no strikes will provide for a durable victory without a political path to invest Sunni Iraqis in Iraq’s future. None of the US air strikes or humanitarian aid drops over the past four days have come anywhere near Baghdad, where the administration has loudly hoped a new government would soon be announced.

The UK’s international development secretary, Justine Greening, said: “The world has been shocked by the plight of the Yazidi community. The UK has acted swiftly to get life-saving help to those affected.”

Also on Sunday, the French foreign minister, Laurent Fabius, met his Iraqi counterpart, Hussein Chahristani, in Baghdad and called for political unity in order to defeat the Islamic extremists rampaging through the country. The establishment of such a government is a high priority for Obama if follow-up strikes aimed at protecting Baghdad or taking territory back from Isis are to be launched, as the US believes Iraqi national unity, elusive over 11 years of war, to be a prerequisite for durable success.

Fabius said a coalition government was necessary to lead the battle against terrorism. “All Iraqis need to be represented so they can fight the terrorism together,” he said after his brief meeting with Chahristani.

Afterwards Fabius travelled to Irbil, where he was due to meet Massoud Barzani, the president of the autonomous Kurdish region, and oversee the delivery of French humanitarian aid for civilian refugees.

President Hollande spoke to Barzani on Saturday by telephone. Political analysts had suggested France was hesitating about whether to join America in carrying out air strikes or stick to emergency aid.

After the call, the Elysée announced the first delivery of emergency food and equipment. “The persecution of religious minorities, namely Christians and Yazidis by this terrorist group, is a crime of extreme seriousness,” it said in a statement.

In a joint editorial in Le Monde, Bernard Kouchner, former Socialist foreign affairs minister, Gérard Chaliand, a writer and specialist in international relations and Frédéric Tissot, former French consul in Irbil, wrote that the Yazidis of Iraq had to be supported to avoid “a genocide” at the hands of the jihadists.

They added: “The international community, the French, Europe, the United States must react immediately to give all those who oppose the barbarity of Isis the means to combat it, but also coordinate humanitarian aid destined for the hundreds of thousands of people who are fleeing its advance.

“When the world is preparing to commemorate the centenary of the Armenian genocide, perpetrated in the neighbouring territory of Ottoman Anatolia, when Christians of the Middle East are threatened everywhere, we cannot let the unthinkable happen once again, we cannot close our eyes to the massacre of the Yazidis of Iraq.”

The return of US air power over Iraq two months after Isis redrew the boundaries of Iraq and Syria – and two and a half years after the US military withdrew from the country – has fuelled recriminations over Obama’s foreign policy that now extend to his potential Democratic successor.

Hillary Clinton, Obama’s first-term secretary of state, 2008 presidential rival and potential 2016 Democratic presidential candidate, gave an interview to the Atlantic excoriating Obama for not confronting Isis earlier. Clinton and the former CIA director David Petraeus reportedly backed an initiative to arm the Syrian rebels years ago, only to see Obama reject it for fear of proliferating weapons to Islamic extremists.

“Great nations need organising principles, and ‘don’t do stupid stuff’ is not an organising principle,’” Clinton told the magazine’s Jeffrey Goldberg, mocking a principle attributed to Obama which he calls geostrategic prudence and his critics call geostrategic lethargy.

“You know, when you’re down on yourself, and when you are hunkering down and pulling back, you’re not going to make any better decisions than when you were aggressively, belligerently putting yourself forward,” said Clinton.

Senator John McCain, a leading Republican voice on foreign affairs, appeared on CNN on Sunday. Citing “a vacuum of American leadership throughout the Middle East”, McCain said that in Iraq there was “the possibility of a cataclysmic scenario and the president says he’s going to protect American troops and prevent a humanitarian catastrophe”.

He said: “That’s not a strategy, that’s not a policy. This is a problem that’s metastasing as we speak.”